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107edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|107}}
{{ED intro}}


== Theory ==
== Theory ==
107edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with four [[mapping]]s possible for the 7-limit: {{val| 107 170 248 300 }} ([[patent val]]), {{val| 107 '''169''' 248 300 }} (107b), {{val| 107 170 '''249''' 300 }} (107c), and {{val| 107 170 '''249''' '''301''' }} (107cd).  
107edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, and [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]] are about halfway between its steps. Either the 2.9.5.7 or 2.9.15.21 [[subgroup]] can be used. For the full 7-limit, it has four possible [[mapping]]s: {{val| 107 170 248 300 }} ([[patent val]]), {{val| 107 '''169''' 248 300 }} (107b), {{val| 107 170 '''249''' 300 }} (107c), and {{val| 107 170 '''249''' '''301''' }} (107cd).  


Using the patent val, it tempers out [[3125/3072]] (magic comma) and 33554432000/31381059609 in the 5-limit; [[1029/1024]], 2240/2187, and 3125/3087 in the 7-limit; [[100/99]], 1232/1215, and 1331/1323 in the 11-limit.  
Using the patent val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo| 28 -22 3 }} in the 5-limit; [[1029/1024]], [[2240/2187]], and [[3125/3087]] in the 7-limit; [[100/99]], 1232/1215, and 1331/1323 in the 11-limit.  


Using the 107b val, it tempers out [[81/80]] (syntonic comma) and {{monzo| -61 -1 27 }}; in the 5-limit; [[2401/2400]], [[2430/2401]], and 234375/229376 in the 7-limit; [[385/384]], 1350/1331, 1375/1372, and 1944/1925 in the 11-limit.  
Using the 107cd val, it tempers out [[1728/1715]], [[4000/3969]], and 28672/28125 in the 7-limit; [[121/120]], [[896/891]], [[1375/1372]], and 3168/3125 in the 11-limit.


Using the 107c val, it tempers out 1638400/1594323 (immunity comma) and 1990656/1953125 (valentine comma) in the 5-limit; [[126/125]], [[1029/1024]], and 307328/295245 in the 7-limit; [[121/120]], [[176/175]], [[441/440]], and 184877/177147 in the 11-limit.  
Using the 107c val, it tempers out 1638400/1594323 ([[immunity comma]]) and 1990656/1953125 ([[valentine comma]]) in the 5-limit; [[126/125]], 1029/1024, and 307328/295245 in the 7-limit; 121/120, [[176/175]], [[441/440]], and 184877/177147 in the 11-limit.  


Using the 107cd val, it tempers out [[1728/1715]], 4000/3969, and 28672/28125 in the 7-limit; 121/120, [[896/891]], 1375/1372, and 3168/3125 in the 11-limit.
Using the 107b val, it tempers out 81/80 ([[syntonic comma]]) and {{monzo| -61 -1 27 }}; in the 5-limit; [[2401/2400]], [[2430/2401]], and 234375/229376 in the 7-limit; [[385/384]], 1350/1331, 1375/1372, and 1944/1925 in the 11-limit.  
 
=== Subsets and supersets ===
107edo is the 28th [[prime edo]].


=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|107}}
{{Harmonics in equal|107}}
=== Octave stretch ===
107edo’s approximations of 3/1, 5/1, 7/1, 13/1, 17/1 and 19/1 are all improved by [[AS|1ed175/174]], a [[Octave stretch|stretched-octave]] version of 107edo. The trade-off is a slightly worse 2/1 and 11/1.
There are also several nearby [[Zeta peak index]] (ZPI) tunings which can be used to improve some harmonics at the expense of others: 622zpi, 623zpi, 624zpi, 625zpi, 626zpi, 627zpi, 628zpi and 629zpi.
The details of each of those ZPI tunings are visible in [[User:Contribution]]’s gallery of [[User:Contribution/Gallery of Zeta Peak Indexes (1 - 10 000)|Zeta Peak Indexes (1 - 10 000)]]. Warning: due to its length, that page may slow down your device while it is open. The effect will go away after you close the page.
=== Subsets and supersets ===
107edo is the 28th [[prime edo]], following [[103edo]] and before [[109edo]]. [[214edo]], which doubles it, provides correction for the approximation to harmonics 3, 5, and 7.


== Intervals ==
== Intervals ==
Line 35: Line 42:
| 2.9
| 2.9
| {{monzo| 339 -107 }}
| {{monzo| 339 -107 }}
| {{val| 107 339 }}
| {{mapping| 107 339 }}
| +0.322
| +0.322
| 0.322
| 0.322
Line 42: Line 49:
| 2.9.5
| 2.9.5
| 9765625/9565938, {{monzo| -34 10 1 }}
| 9765625/9565938, {{monzo| -34 10 1 }}
| {{val| 107 339 248 }}
| {{mapping| 107 339 248 }}
| +0.933
| +0.933
| 0.904
| 0.904
Line 49: Line 56:
| 2.9.5.7
| 2.9.5.7
| 225/224, 84035/82944, {{monzo| 14 -6 7 -4 }}
| 225/224, 84035/82944, {{monzo| 14 -6 7 -4 }}
| {{val| 107 339 248 300 }}
| {{mapping| 107 339 248 300 }}
| +1.087
| +1.087
| 0.827
| 0.827
Line 56: Line 63:
| 2.9.5.7.11
| 2.9.5.7.11
| 225/224, 441/440, 26411/26244, 161280/161051
| 225/224, 441/440, 26411/26244, 161280/161051
| {{val| 107 339 248 300 370 }}
| {{mapping| 107 339 248 300 370 }}
| +0.973
| +0.973
| 0.774
| 0.774
Line 63: Line 70:
| 2.9.5.7.11.13
| 2.9.5.7.11.13
| 225/224, 325/324, 441/440, 847/845, 24500/24167
| 225/224, 325/324, 441/440, 847/845, 24500/24167
| {{val| 107 339 248 300 370 396 }}
| {{mapping| 107 339 248 300 370 396 }}
| +0.783
| +0.783
| 0.823
| 0.823
Line 70: Line 77:
| 2.9.5.7.11.13.17
| 2.9.5.7.11.13.17
| 170/169, 225/224, 325/324, 441/440, 847/845, 2000/1989
| 170/169, 225/224, 325/324, 441/440, 847/845, 2000/1989
| {{val| 107 339 248 300 370 396 437 }}
| {{mapping| 107 339 248 300 370 396 437 }}
| +0.812
| +0.812
| 0.765
| 0.765
| 6.82
| 6.82
|}
|}
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